Gauss-Bonnet solution with a cloud of strings in de Sitter and anti-de Sitter space

Abstract: In this paper, we present exact spherically symmetric Gauss-Bonnet black hole solutions surrounded by a cloud of strings fluid with cosmological constant in $D>4$ dimensions. Both charged and uncharged cases are considered. We focus on the de Sitter solutions in the main text and leave the Anti-de Sitter solutions in the appendix. We analyze the features of thermodynamic properties of the black hole solutions. The mass, Hawking temperature as well as thermal stability and the phase transitions are discussed. Moreover, the equation of state and critical phenomena associated with these solutions are also explored.